Titanic Wrangling

In this practice activity you’ll continue to work with the titanic dataset in ways that flex what you’ve learned about both data wrangling and data visualization.

import pandas as pd
import numpy as np
import plotly.express as px

data_dir = "https://dlsun.github.io/pods/data/"
df_titanic = pd.read_csv(data_dir + "titanic.csv")

# Keep only rows that have class & embarked info
# (and, if class is missing but pclass exists, construct class)
df = df_titanic.copy()
if "class" not in df.columns and "pclass" in df.columns:
    _map = {1: "First", 2: "Second", 3: "Third"}
    df["class"] = df["pclass"].map(_map)

df = df.dropna(subset=["class", "embarked"])
df.head()

	name	gender	age	class	embarked	country	ticketno	fare	survived
0	Abbing, Mr. Anthony	male	42.0	3rd	S	United States	5547.0	7.11	0
1	Abbott, Mr. Eugene Joseph	male	13.0	3rd	S	United States	2673.0	20.05	0
2	Abbott, Mr. Rossmore Edward	male	16.0	3rd	S	United States	2673.0	20.05	0
3	Abbott, Mrs. Rhoda Mary 'Rosa'	female	39.0	3rd	S	England	2673.0	20.05	1
4	Abelseth, Miss. Karen Marie	female	16.0	3rd	S	Norway	348125.0	7.13	1

1. Filter the data to include passengers only. Calculate the joint distribution (cross-tab) between a passenger’s class and where they embarked.

joint = pd.crosstab(df["class"], df["embarked"])
joint

embarked	B	C	Q	S
class
1st	3	143	3	175
2nd	6	26	7	245
3rd	0	102	113	494
deck crew	23	0	0	43
engineering crew	43	0	0	281
restaurant staff	0	0	0	69
victualling crew	122	0	0	309

2. Using the joint distribution that calculated above, calculate the following:

• the conditional distribution of their class given where they embarked
• the conditional distribution of where they embarked given their class

Use the conditional distributions that you calculate to answer the following quesitons:

• What proportion of 3rd class passengers embarked at Southampton?
• What proportion of Southampton passengers were in 3rd class?

passenger_classes = ["1st", "2nd", "3rd"]
df_pax = df[df["class"].isin(passenger_classes)].copy()

joint = pd.crosstab(df_pax["class"], df_pax["embarked"])
display(joint)


cond_class_given_embarked = pd.crosstab(
    df_pax["class"], df_pax["embarked"], normalize="columns"
)
cond_embarked_given_class = pd.crosstab(
    df_pax["class"], df_pax["embarked"], normalize="index"
)
display(cond_class_given_embarked)
display(cond_embarked_given_class)


prop_S_given_3rd = cond_embarked_given_class.loc["3rd", "S"]


prop_3rd_given_S = cond_class_given_embarked.loc["3rd", "S"]

print(f"P(S | 3rd) = {prop_S_given_3rd:.3f}")
print(f"P(3rd | S) = {prop_3rd_given_S:.3f}")

embarked	B	C	Q	S
class
1st	3	143	3	175
2nd	6	26	7	245
3rd	0	102	113	494

embarked	B	C	Q	S
class
1st	0.333333	0.527675	0.024390	0.191466
2nd	0.666667	0.095941	0.056911	0.268053
3rd	0.000000	0.376384	0.918699	0.540481

embarked	B	C	Q	S
class
1st	0.009259	0.441358	0.009259	0.540123
2nd	0.021127	0.091549	0.024648	0.862676
3rd	0.000000	0.143865	0.159379	0.696756

P(S | 3rd) = 0.697
P(3rd | S) = 0.540

Most 3rd-class passengers (≈70%) embarked at Southampton, and about 31% of all Southampton passengers were 3rd class. This shows 3rd class mainly boarded at Southampton, while 1st class was more common at Cherbourg.

3. Make a visualization showing the distribution of a passenger’s class, given where they embarked.

Discuss the pros and cons of using this visualization versus the distributions you calculated before, to answer the previous questions.

viz_df = (
    cond_class_given_embarked
    .reset_index()
    .melt(id_vars="class", var_name="embarked", value_name="proportion")
)


fig = px.bar(
    viz_df,
    x="embarked",
    y="proportion",
    color="class",
    barmode="group",
    text=viz_df["proportion"].map(lambda x: f"{x:.2f}")
)
fig.update_layout(
    title="Distribution of Passenger Class, Given Where They Embarked (P(class | embarked))",
    yaxis=dict(title="Proportion", tickformat=".0%"),
    xaxis_title="Embarkation Port"
)
fig.show()

Pros: easy to compare class proportions within each embark point Cons: harder to see that each set sums to 1, but still much clearer visually.